Why is one of the lines / edges visible on my mirror
If you (try to) select one of the triangles defined by the problematic edge, you will see that it's actually a quad:

So the edge there is not defining any face. Blender doesn't display edges defining faces in Object Mode, but it does display edges that don't define a face. In a way your problem proves the usefulness of this approach, as thanks to that, you noticed a problem with your topology.
You can simply select the edge and press X, then E to remove it. If you want to divide this quad into two triangles, then after removing current edge select appropriate vertices and press J to Join them. This will cut through the existing face like with a knife tool, instead of adding an edge on top of existing topology without changing it.